Here is the full list of all 38 Rune Factory: Tides of Destiny trophies - there are 21 bronze, 12 silver, 4 gold and 1 platinum.
Earn all trophies.
Achieve repeat victories in the colloseum.
Successfully land 2000 fish.
Catch a cold 100 times.
Consume 100 recovery drinks.
Successfully land 1000 fish.
Win a battle in the colloseum.
See the true face of the man in the mask.
Defeat the Legendary Golem.
Lift the stone curse from the Water Temple.
Lift the stone curse from the Fire Temple.
Lift the stone curse from the Earth Temple.
Find out what's wrong with the Plant Golem and get him working again.
Earn the goodwill of many residents on Fenith Island.
Defeat 5000 monsters.
Raise all of the islands out of the sea.
Defeat 30 giant monsters.
Defeat 20 giant monsters.
Defeat 3000 monsters.
Successfully salvage 30 times.
Defeat 10 giant monsters.
Successfully salvage 20 times.
Successfully land 300 fish.
Successfully salvage 10 times.
Defeat 1500 monsters.
Successfully craft 1500 items.
Listen to Maerwen's explanation about trophies.
Successfully craft 800 items.
Defeat 500 monsters.
Perform a double-jump 500 times.
Successfully craft 300 items.
Successfully land a fish.
Get to the bottom of why Sprout Island turned to stone.
Stay awake until you collapse at 5AM.
Defeat 100 monsters.
Fail at cooking one time.
Successfully craft an item.
Use the Plant Golem to raise an island out of the sea.